The U(1) Lattice Gauge Theory Universally Connects All Classical Models with Continuous Variables, Including Background Gravity

TL;DR

This paper demonstrates that a wide class of classical models with continuous variables, including those with background gravity, can be represented as a four-dimensional U(1) lattice gauge theory, unifying diverse models under a common framework.

Contribution

It introduces a universal mapping of classical models with continuous degrees of freedom to a 4D U(1) lattice gauge theory, even in curved spacetime backgrounds.

Findings

Classical models' partition functions can be expressed as U(1) LGT partition functions.

U(1) LGT in curved spacetime maps to flat background models.

The approach uses an inner product of quantum states to establish the mapping.

Abstract

We show that the partition function of many classical models with continuous degrees of freedom, e.g. abelian lattice gauge theories and statistical mechanical models, can be written as the partition function of an (enlarged) four-dimensional lattice gauge theory (LGT) with gauge group U(1). This result is very general that it includes models in different dimensions with different symmetries. In particular, we show that a U(1) LGT defined in a curved spacetime can be mapped to a U(1) LGT with a flat background metric. The result is achieved by expressing the U(1) LGT partition function as an inner product between two quantum states.